Interpretation help - Coefficient of GINI

[Fahad Mirza]

Hello everyone.

I am looking to interpret a regression where dependent variable is a efficiency score calculated using DEA (Bounded between 0 and 1) and one of the independent variables is a GINI (Bounded between 0 and 1)

Summary Stats:

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
      theta1 |        117    .4201543    .2141238   .0235029          1
        gini |        115    .2167834    .0490994   .1193491   .3518247

Coefficient:

Simar & Wilson (2007) eff. analysis      Number of obs             =       106
(algorithm #1)                           Number of efficient DMUs  =         4
                                         Number of bootstr. reps   =      1000
inefficient if theta1 < 1                Wald chi2(5)              =     27.42
onesided truncation                      Prob > chi2(5)            =    0.0000

------------------------------------------------------------------------------
Data Envelopment Analysis:                         externally estimated scores

------------------------------------------------------------------------------
             |  Observed   Bootstrap                           Percentile
  efficiency |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
theta1       |
        gini |   1.238968    .400295     3.10   0.002     .4559526    2.042307

The model does not contain any interactions or square terms and has other variables included.

[Maarten Buis]

The name of your variable makes me worried: Is exp_gini the Gini coefficient or exp(Gini), i.e. e to the power of Gini?

[Fahad Mirza]

Hi Maarten,

Sorry for the confusion this is GINI calculation and not an exponent. The variable name is just for my own reference. I will also edit the main post and remove "exp_"

[Maarten Buis]

Thank you, that is clear now. So I suspect that your worry is that the coefficient is larger than 1 while the dependent variable only ranges between 0 and 1. Is that correct?

[Fahad Mirza]

Precisely, thats the issue I had in mind regarding it when trying to interpret.

[Maarten Buis]

In a regression the coefficient means the change in expected value of y for a unit change in x. The unit is thus important. In case of a Gini coefficient a unit change is going from completely equal (everybody has exactly the same amount) to completely unequal (one person has everything). That is a pretty extreme change, and it is to be expected that pretty extreme changes have pretty extreme consequences. That is what you are seeing. It is also an extrapolation in this case; you don't have observations with a Gini of 0 or a Gini of 1 in your data. In your case I would just multiply the variable gini by 10 and add that variable to your model instead. Now the unit of that new variable is 0.1 Gini point change. That is still a very big change, but not so outrageous as a 1 Gini point change. Notice that you are not changing the model that way, you are only changing the unit of one of the variables.